Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10602088 | C2 | semidirect |
| 2. #10602083 | C2 | semidirect |
| 3. #10600098 | C2 | semidirect |
| 4. #10600093 | C2 | semidirect |
| 5. C5×#1357 | C2 | semidirect |
| 6. #10598062 | C2 | semidirect |
| 7. #10598057 | C2 | semidirect |
| 55. #1357 | D5 | semidirect |
| 205. C5 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602088 | 2 |
| #10602083 | 2 |
| #10600098 | 2 |
| #10600093 | 2 |
| C5×#1357 | 2 |
| #10598062 | 2 |
| #10598057 | 2 |
| #12436 | 5 |